Question: The equation of a circle $C$ is $x^2+y^2+16x+4y+32 = 0$. What is its center $(h, k)$ and its radius $r$ ?
Answer: To find the equation in standard form, complete the square. $(x^2+16x) + (y^2+4y) = -32$ $(x^2+16x+64) + (y^2+4y+4) = -32 + 64 + 4$ $(x+8)^{2} + (y+2)^{2} = 36 = 6^2$ Thus, $(h, k) = (-8, -2)$ and $r = 6$.